09 target and clutter characteristics

8/6/2019 09 Target and Clutter Characteristics

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Chapter 9.

Target and Clutter Characteristics

9.1. Target Cross SectionThe cross section qualitatively relates the amount of power that strikes the target to theamount of power that is reflected into the receiver. Assuming that the power density of a plane wave incident on the target is Si W/m

2, and the amount of power scattered

isotropically isPrwhich is defined in terms of the cross section, , as follows

ir SP .= . (9.1)

Then the power density Srof the scattered wave at the receiving antenna is

24 R

PS rr

= . (9.2)

This allows the cross section to be defined in terms of the ratio of the power density at thereceiver to that incident on the target

i

r

S

SR24 = . (9.3)

And in order to ensure that the receiving antenna is in the far field and that the waves areplanar

i

r

R S

SR24lim = . (9.4)

In terms of the various fields and pressures that make up EM and acoustic waves, thisequation can be expanded as follows,


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Because complex targets are made up from many scattering surfaces the cross sectionwill also be made up of reflections from a large number of scatterers,. This means thateven very small changes in the aspect angle of the target will result in relative phase

changes between the scatterers and an altered cross section. The effective surface

roughness of a target (as a function of) also plays an important roll in determining itscross section. There are three mechanisms that determine individually, or in combination,the target reflection characteristics.

Diffuse Reflection Specular Reflection Retro Reflection

Figure 9.1: Different modes of reflection depend on the surface characteristics of the target

There are a number of significant differences between the cross sections of targetsmeasured using EM waves and those measured using acoustic waves, though theunderlying theory of reflection is the same in the two cases

9.2.

Radar Cross Sections (RCS)Qualitatively, the RCS of an object is a measure of its size as seen at a particular radarwavelength and polarisation. RCS has units of m2 and is often expressed in decibelsrelative to a square meter (dBm2)

)(log10)( 2102 mdBm = . (9.6)

To account for the polarisation dependency of RCS, the relationship between thetransmitted and received electric fields must be considered in terms of their orthogonallinear polarisation components EH and EV. and the proportionality constants that relatethem.

=

t

V

t

H

VVHV

VHHH

r

V

r

H

E

E

aa

aa

E

E. (9.7)

This matrix of constants is referred to as the target scattering matrix and it can be used tojustify the definition of a radar cross section scattering matrix with the same form.

=

VVHV

VHHH

. (9.8)


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The relationship between the target and RCS scattering matrices is as follows (for each ofthe four terms)

HHjHHHH ea

= , (9.9)

where ij - magnitude of each matrix component,

ij - Phase of the associated element.

From hereon the target RCS will be considered to have a single value that corresponds to

eitherHHorVVdepending on the transmitted polarisation.

9.3. RCS of Simple ShapesA number of simple reflectors are useful, particularly for use as calibration targets. Theflat plate offers the highest RCS for a given size, but it is specular which makes itdifficult to align. An alternative is the trihedral corner-reflector which also produces ahigh RCS which remains reasonably constant over a wide angle. This is the preferredRCS reference.

The sphere is also often used as a reference for moving targets as its RCS is invariantwith observed angle. Unfortunately the RCS is very small for its size and also largeconductive perfect spheres are difficult to manufacture.

9.3.1. Flat PlateThe flat plate has the largest peak RCS for its size of any target, It is specular and so the

RCS falls off sharply with changes in incidence angle from 0. The length, a, of the platedetermines the width of the specular lobe and the interval between peaks as defined by

2

2

cos

sin2

sin2

sin

)(

=a

a

o (9.10)

2

22

4 bao = (9.11)

where () RCS as a function of angle (m2),

a,b Sides of the plate (m),

- Plate rotation around M axis (rad).

At incidence angles close to 90, complex edge diffraction effects become dominant andsmall irregularities in the surface destroy the symmetry of the data in the followingfigure.


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Figure 9.2: Measured RCS of a flat square plate as a function of orientation

9.3.2. The SphereA perfectly conducting sphere is the simplest shape whose RCS can be determined

exactly. With its 3D symmetry its RCS is aspect independent, so is often used as acalibration target if the size is selected appropriate to the operating frequency of themeasurement system.

Figure 9.3: RCS of a sphere as a function of the circumference normalised by the wavelength of the

incident radiation.


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Note that there are three regions that are apparent from this figure:

Rayleigh Region (2a/ < 1): The RCS is inversely proportional to the 4th powerof the wavelength as indicated by the slope of the curve in that region.

Mie Region (1 < 2a/ < 10): In this resonance region, a creeping wave travelsaround the sphere and back towards the receiver where it interferes constructivelyor destructively with the specular backscatter to produce a cyclical variation in theRCS

Optical Region (2a/ > 10): The RCS of the sphere approaches its geometricprojected area a2.

9.3.3. Trihedral ReflectorTrihedral corner reflectors have large non-specular radar cross sections and so make idealas a test targets as alignment is not critical. Their behaviour for linear polarisations isgood, but they cannot be used for circularly polarised measurements as the triple bouncereverses the sense of the polarisation. For a symmetrical reflector having each vertex withlength a, the peak radar cross section is determined by

2

4

3

4

a= . (9.12)

Figure 9.4: RCS of a trihedral reflector as a function of orientation

From the figure it can be seen that azimuth and elevation misalignments of up to about

10 can be tolerated without a significant reduction in RCS


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9.3.4. Other simple reflectorsTable 9.1: Maximum RCS for typical calibration targets

Target MaximumCross Section

Advantages Disadvantages

Cylinder

22 ab=

Nonspecular alongthe radial axis

Low RCS for size,specular along axis

Sphere 2a = Nonspecular Lowest RCS for size,radiates isotropically

Diplane2

228

ba=

Large RCS forsize, nonspecularalong one axis.Useful for testingpolarisation

Specular along oneaxis

TriangularTrihedral 2

4

3

4

a=

Nonspecular Cannot be used forcross polarisedmeasurements

Square

Trihedral 2

412

a

=

Large RCS for

size, nonspecular

Cannot be used for

cross polarisedmeasurements

CircularTrihedral 2

43507.0

a=

Large RCS forsize, nonspecular

Cannot be used forcross polarisedmeasurements

FlatRectangularPlate

2

224

ba=

Largest RCS forsize

Specular along bothaxes, difficult toalign

Top Hat Low RCS for size Difficult to alignrotated seam

Bruderhedral

3

2

cos2 ab=

is the elevation angleto the cylinder, =0 is

perpendicular to thecylinder

c>b to be effective

for 90 rotation ofpolarisation = 45

Large RCS, easierto align for rotationthan Top Hat

Moderately specularalong one axis


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9.4. RCS of Complex Targets9.4.1. AircraftThe RCS of full size aircraft can be measured in an outdoor range by placing the aircrafton a pedestal mounted on a turntable. To reduce the mass of such targets they are oftengutted. However this can introduce inaccuracies in the results as jet engines and cockpitinstrumentation often add a significant contribution to the overall RCS.

The following figure shows the now classic radar cross section of a B-26 bomber plottedon polar axes as a function of azimuth angle. Note that the RCS exceeds 35dBm

2

(3100m2) from certain aspect angles. In contrast the RCS of the B2 stealth bomber isabout 40dBm2.

Figure 9.5: Diagram and radar cross section of a B-26 bomber as a function of aspect angle

A more modern aircraft, the C29 cargo plane shows a more dramatic variation in the RCS

with strong peaks at +/-90, generated by the aircraft fuselage. From the tail-on aspect,this aircraft also shows a reasonably large RCS that may be generated by the engineoutlets.

Figure 9.6: RCS of a C29 cargo plane with aspect angle


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9.4.2. Ships

2.8GHz

9.225GHz

Figure 9.7: RCS of a naval auxiliary ship with aspect angle

Measuring the RCS of a ship involves sailing in a circle while measuring the return froma fixed point and then compensating for variations in range as it is not practical to mountships on turntables.

The median RCS of a typical ship at low grazing angles (excluding the specularbroadside return) is related to its size by the empirical formula

23

21

52 Df= m2, (9.13)

where:f frequency (MHz),D displacement (kilotons).

At higher grazing angles, the median RCS is equal to the displacement tonnage expressedin m

2.

Radar measures range andreturn amplitude

Boat sails ina tight circle and

transmits itscompass bearing

to the shore Data acquisition unitlogs radar output and

bearing of boat

200m

Figure 9.8: Polar RCS measurement setup


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The empirical relationship described in (9.13) is not considered to be accurate at highfrequencies due to the quadratic increase in the RCS of simple targets (flat plates andcorners) with increasing frequency. We have measured the RCS of a number of small

boats at 94GHz from a shore-mounted radar that tracked the craft in angles as it sailedslowly in a tight circle at an appropriate range.

The radar measured and logged the returns from the target, while the boat angle measuredby an electronic compass on board, was communicated back to the shore where it wasalso logged. The data was then used to produce a polar RCS measurement such as the oneshown in the following figure.

Figure 9.9: RCS of a Steber42 flybridge cruiser at 94GHz at a 2.5 grazing angle

It is interesting to note that the median RCS of this boat is about 10dBm2, and the RCS

calculated using (9.13) for a 13 ton displacement and a frequency of 94GHz comes out at13dBm2

9.4.3. Ground VehiclesMeasurement techniques for ground vehicles generally involve measuring the RCS

through 360 in azimuth by rotating the vehicle on a turntable. These are normally madefrom a reasonably short range so that it is possible to produce plots at various grazingangles by adjusting the height of the measurement radar.


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Figure 9.10: RCS of a Toyota utility vehicle at 35GHz from a 0 grazing angleFor the measurements made by us shown below, a turntable was not available, so thevehicle was driven slowly in a tight circle while the radar measurement system wasaimed manually.

Armoured Personnel Carrier Bedford Truck

Figure 9.11: RCS of larger military vehicles at 94GHz

The RCS of military vehicles is often larger than that of military aircraft because thelatter are generally more rounded for aerodynamic reasons,. Ground vehicles are oftenmade up of flat armour plates and lots of brackets, antennas etc.


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9.5. RCS of Living Creatures9.5.1. Human BeingsThe RCS of a human being is a function of frequency as shown in the following table.Variations are with aspect angle and polarisation.

Table 9.2: RCS of a human being at different frequencies

Frequency (MHz) RCS (m2)

410 0.033 2.331120 0.098 0.997

2890 0.140 1.05

4800 0.368 1.88

7375 0.495 1.22

Some of our measurements of the human torso with a spot size of 1.3m made at 94GHzare reproduced below. They show a lower value for the RCS than those predicted fromthe table.

The measurements include a reference 1m2

reflector in the beam about a metre off theground that is eclipsed as the human subject walks into the beam directly in front of it.

Radar

Person

Figure 9.12: Measuring RCS of human beings

Figure 9.13: Human RCS at 94GHz is determined by having a person block the path from the radar

to the 0dBsqm corner reflector. The RCS is determined by the decrease in the signal level

It can be seen from these measurements that the RCS of the two human beings variesbetween 3dB and 8dB lower than the 1sqm (0dBsqm) reflector at 94GHz.


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9.5.2. BirdsRadar returns are often returned from areas that appear clear, these are called ghosts or

angles. They are often returns from flocks of birds or swarms of insects. Because birdscan fly at up to 50knots their returns are not rejected by Doppler or MTI (Moving TargetIndicator) processing.

Table 9.3: RCS of birds as a function of frequency

Bird Type Frequency Mean RCS

(cm2)

Median RCS

(cm2)

X 16 6.9

S 25 12

Grackle

UHF 0.57 0.45

X 1.6 0.8

S 14 11

Sparrow

UHF 0.02 0.02

X 15 6.4

S 80 32

Pigeon

UHF 11 8.0

Note that resonance effects play a large role in the measured RCS of the birds shownhere. This is verified in the following graph that relates bird mass to RCS.

Figure 9.14: Bird RCS at 3GHz

Fluctuations in the RCS of a single bird in flight have been measured to have a log-normal distribution and an empirical formula that relates the wing beat frequency, f (Hz)

of birds to their length, l (mm) is 572. 827.0 =lf .


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9.5.3. InsectsAppreciable echoes are only obtained from

insects if their body length exceeds /3.Insects viewed broadside have RCS valuesbetween 10 and 1000 times larger than whenviewed head on.

At X-band the RCS of a variety of insectsshowed a variation from 0.02 to 9.6cm2 withlongitudinal polarisation and between 0.01and 0.95cm2 for transverse.

A bee would have a broadside RCS of about

1cm2 at X-band. This would not increasesignificantly up to W-band as the bee movedfrom the Mie to the Optical region

Figure 9.15: RCS of insects at 9.4GHz.

Line shows RCS of a water droplet

9.6. Fluctuations in RCS9.6.1. Temporal FluctuationsIf either the radar or the target is moving, variations in the aspect angle result influctuations in the RCS. These fluctuations have a major effect on the probability ofdetection of a target as discussed in Chapter 10.

Figure 9.16: Log plot of the Rayleigh distribution


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The RCS of a target, such as the Toyota Utility Vehicle described above, can be

displayed as a probability density function based on the full 360 azimuth coverage, or asmaller sector if required. Though these are in effect spatial variations in RCS, if thevehicle is moving and showing a changing aspect to the radar, then they map intotemporal variations.

Figure 9.17: PDF and cumulative probability distributions of the RCS of a Toyota at 35GHz

A single value for RCS is often used to characterise a target. The mean or median are themost common values selected for this purpose.

9.6.2. Spatial Distribution of Cross SectionThe various reflecting bodies across a target interfere constructively and destructively asit moves. This results in a physical displacement of the effective target position thatvaries with time. The angular position of the target measured by a radar system isdetermined by the direction-of-arrival of the phase front of the reflected radar signal fromall scatterers, and so it is possible that the angular error can extend beyond the physicalboundaries of the target. These variations in direction of arrival are known as glint.

The graph below shows a sample of the angular tracking error measured for an aircraftflying towards the radar.

Figure 9.18: Displacement of the tracked centroid of an aircraft echo with time illustrates a

phenomenon known as glint


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Assuming that the aircraft path is undisturbed, and can be approximated by the meanvalue of this signal, then if the extent of the tracking error is compared to the physicalextent of the aircraft, it is found that the PDF extends past the wingtips as shown below.

Figure 9.19: Probability distribution function of the angle tracking error

Measured glint spectra show that a significant portion of the return occurs at frequenciesbelow 3Hz. This is within the bandwidth of most tracking filters, and so glint can causeserious tracking errors if the appropriate precautions are not taken (see Chapter 13).

9.7. Radar StealthStealth in this context is the ability of an aircraft to evade radar, however that is only oneof several factors that must be considered to keep aircraft undetected. The others can bealmost as important and include the following:

Sound Sight Heat Leaking electronic signals


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Figure 9.20: Major contributors to radar cross section of a jet fighter

The basics of stealth have been known since the 1950s and the computational powerrequired to design stealth aircraft has been available since the 1970s. These requirementsdictate the shape of modern stealthy aircraft are summarised in the figure below.

Figure 9.21: Designing aircraft for stealth

The first stealth aircraft relied on faceting to reflect power away from its source. This iseffective against monostatic systems, but it is not effective against bistatic, or multistaticsystems where the transmitter and receiver are spatially separated.


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Anti stealth technology includes the following techniques:

Radar with wavelengths longer than the aircraft. Bistatic and multi static radar configurations. These can use dedicated

transmitters or existing FM or mobile phone broadcasts.

Wide-band radar as it is difficult to make good wide-band RAM. Wake and exhaust detection and tracking, as neither of these can be

completely eliminated.

Wingtip vortex detection as vortices generate turbulence that changes therefractive index of the air, and so reflects radar signals.

9.7.1. Stealth Foiled by Cell Phone NetworkAmericas multi-billion-dollar stealth bombers could be rendered obsolete by a British invention that uses existing mobiletelephone masts to detect and track aircraft that were previously invisible to radar.

US stealth fighters and bombers such as the F117, B1 and B2 played key roles in the Gulf and Kosovo wars as they arealmost impossible to detect using conventional radar.

However, the ease with which the mobile telephone mast system developed at a laboratory in Hampshire can be usedto detect the aircraft has greatly concerned the military.

Peter Lloyd, the head of projects at Roke Manor Research, said: I cannot comment in detail because it is a classifiedmatter, but lets say the US military is very interested.

Stealth aircraft, each of which costs at least $A3.6 billion, are shaped to confuse radar. A special paint absorbs radiowaves, reducing the radar signature to the equivalent of a gull in flight

The Roke Manor scientists discovered that telephone calls sent between mobile phone masts detected the preciseposition of stealth aircraft with ease. We use just the normal phone calls that are flying about in the ether, Lloyd said.The front of the stealth plane cannot be detected by conventional radar, but its bottom surface reflects very well.

Mobile telephone calls bouncing between base stations produce a screen of radiation. When the aircraft fly through thisscreen they disrupt the phase pattern of the signals. The Roke Manor system uses receivers, shaped like televisionaerials, to detect distortions in the signals.

A network of aerials large enough to cover a battlefield can be packed in a Land Rover.

Using a laptop connected to the receiver network, soldiers on the ground can calculate the position of stealth aircraft withan accuracy of 10 metres with the aid of the GPS satellite navigation system.

Its remarkable that a stealth system that cost 60 billion [$158 billion] to develop is beaten by 100,000 mobile phone technology,

Mr Lloyd said. Its almost impossible to disable a mobile phone network without bombing an entire country, whereas radar

installations are often knocked out of action with a single bomb or missile.

9.8. Stealth and Frequency AllocationAccording to Barry Fox (New Scientist 31 August 2002), satellite based TVcommunications bandwidth is almost exhausted in the X-band and frequency has beenallocated in the Ku-Band (12-18GHz). This band falls directly within the bandtransmitted by the radar of the B2 stealth bomber, and so not only would the high

powered radar advertise the presence of the aircraft, but it could even damage sensitivereceivers on the ground.

It will cost at least $1 billion to upgrade the radar


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Figure 9.24: B2 stealth bomber

9.9. Complex Targets at IR and Visible FrequenciesThe primary differences between radar and laser target characteristics are as follows:

Laser targets are generally larger than the beam footprint Targets which appear smooth at microwave frequencies will appear rough at

higher frequencies

A diffuse surface at microwave may appear as a collection of specular scatterersto a laser

For a laser, the scattering cross section is

=GA, (9.14)

where: - Cross Section (m2),

- Reflectivity of the surface,G Gain of target,A Projected physical area (m

2).

The gain is given by

==

442

cAG , (9.15)

where:Ac Area of coherence - 2/,

- Solid angle spread of the reflected light around the direction between the laser

and the target.

On a scattering surface of physical areaA, there are Mindependent coherence areas suchthat M= A/Ac. For coherent scattering M= 1 orM>> 1. For intermediate values ofM,interference between coherence areas must be considered.

ForM= 1, a specular scatterer

2

24

A= . (9.16)


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ForM>> 1, the diffuse surfaces from which, according to Lamberts Law, the scattered

power density decreases proportional to cos(), where is the angle from the surface

normal. In this case = and = 4Acos().

Figure 9.25: Lambertian scatterer

Instead of using cross section to define the characteristics of a laser target, distributed

targets are often characterised by their reflection coefficient (as discussed in Chapter 6)and physical cross section.

The reflection coefficient is a function of frequency, so the tables reproduced earlier for

microwave and 10m infrared will not be the same as those for 0.9m infrared shown inthe table below.

Table 9.4: IR reflectivity of various materials at 0.9mDiffusely Reflecting Material Reflectivity (%)

White paper Up to 100

Cut clean dry pine 94

Snow 80-90

Beer foam 88

White masonry 85

Limestone, clay Up to 75

Newspaper with print 69

Tissue paper 2-ply 60

Deciduous trees Typ 60

Coniferous trees Typ 30

Carbonate sand (dry) 57

Carbonate sand (wet) 41

Beach sand and bare desert Typ 50

Rough wood pallet (clean) 25

Smooth concrete 24Asphalt with pebbles 17

Lava 8

Black neoprene 5

Black rubber tyre wall 2

Specular Reflecting Material

Reflecting foil 3M2000X 1250

Opaque white plastic1 110

Opaque black plastic1 17

Clear plastic1 50

1 Measured with the beam perpendicular to the surface to achieve maximum reflection


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For a diffuse scatterer, the reflection coefficient cannot exceed 100% but for a specularscatterer, the reflection coefficient can be many times this value. Manufacturers of laserrange finders generally specify their performance for a target with 80% diffuse

reflectivity.

9.10.Complex Acoustic Targets9.10.1.Target CompositionAs with electromagnetic radiation, in the acoustic domain, all materials will partiallyreflect, partially absorb and partially transmit the incident acoustic pulse. This isquantified by the coefficient of reflectivityKrof the target

2

+

==oa

oa

i

rr

ZZ

ZZ

I

IK , (9.17)

where:Ir Reflected intensity of the sound,II Incident intensity of the sound,Za Acoustic impedance of air,Zo Acoustic impedance of object (target).

As the acoustic impedance Zo is related to the propagation velocity, hard dense targetstend to reflect well (as their propagation velocity is high), while soft light targets tend totransmit or absorb.Zo is not only a function of the target material, but also its texture.

Lower frequencies are often absorbed by porous targets and so air, it is generally best tooperate at the highest frequency that will propagate effectively.

9.10.2.Target PropertiesWhile material properties are important at a microscopic level, the acoustic pulseinteracts with a relatively large area of the target, so the strength and quality of an echofrom the target will depend on its geometry. For short range applications where theinsonified footprint is smaller than the target extent, shape is important because manytargets are specular in nature (walls etc.)

normal surfaceoblique surface

diffuse surface

Figure 9.26: Rough and smooth scatterers


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As the frequency increases, the effective surface roughness, as a function of the acousticwavelength, increases and targets become less specular. As a rule of thumb, theamplitude of the signal reflected from a target will increase with its size until it is

approximately 10across.

One of the major issues with short range ultrasound sonar applications, particularly instructured environments like the interiors of buildings, is that the walls are specular andthe corners are retro reflectors. These characteristics, in conjunction with a significantmultipath problem, results in extremely confusing returns. It can be seen in the figurebelow that most of the returns are either from corners, the walls at normal incidence or asa result of multiple bounce echoes from corners via the walls at oblique angles.

Figure 9.27: Effect of specular reflection on sonar scans for a smooth walled room

From these results it is obvious that the use of this technology for indoor navigation isfraught with difficulty if the observation is made from a single position. However, by


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fusing the results of multiple scans made from different positions within the room, abetter match between the measured and true interior is possible.

9.10.3.Particulate TargetsMany acoustic systems are used for industrial applications such as level measurement inbins or silos. The target in these instances are often particulate in nature and it has twocharacteristics that are important as regards the echo strength:

Small scale granularity Large scale angle of repose and undulation.

Granularity

Granular particles scatter the reflected wave in all directions which is essential for anecho return if the material is lying at an angle to the normal. If, however, the particle size

is comparable to /2, then significant cancellations can occur.

As a rule of thumb, the acoustic wavelength should be chosen to exceed the grain size bya factor of four.

Angle of Repose and Undulations

If the material surface lies at an angle to the incident acoustic wave, the echo can bereflected away from the transducer towards the walls of the vessel. This can result in theecho return following a zig-zag path and an incorrect range reading.

With an undulating surface in which the period of the undulations is shorter than beamfootprint, the echo can be directed to follow multiple paths back to the transducer whichcan spread the pulse and result in a lower probability of detection.


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9.11.ClutterOne complicating factor in the study of clutter is that it means different things in differentsituations. For example, to an engineer developing a missile to detect and track a tank, thereturn from vegetation and other natural objects would be considered to be clutter.However, a remote sensing scientist would consider the return from natural vegetation asthe primary target. Clutter is thus defined as the return from a physical object or a groupof objects that is undesired for a specific application.

Clutter may be divided into sources distributed over a surface (land or sea), within avolume (weather or chaff) or concentrated at discrete points (structures, birds orvehicles).

9.12.Surface ClutterThe magnitude of the signal reflected from the surface back to the receiver is a functionof the material, roughness and angle. There are three primary scattering types into whichclutter is generally classified. These are specular, retro and diffuse as shown in the figuresbelow.

Figure 9.28: Specular clutter in which most of the signal is reflected away from the radar because the

surface is smooth compared to the transmitted wavelenght

Figure 9.29: Retro clutter in which a large portion of the signal is returned to the radar due to the

configuration of multiple reflecting surfaces


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Figure 9.30: Diffuse clutter in which the signal is reflected in all directions with the result that a small

fluctuating proportion is reflected back to the radar

9.12.1.Ground ClutterBecause of the statistical nature of clutter, the mean reflectivity is most often quoted. Aconvenient mathematical way to describe this mean value for surface clutter is the

constantmodel in which the surface reflectivity is modelled as

sin=o , (9.18)

where o Reflectivity (cross section per unit area m2/m2),- Grazing angle at the surface (rad),

- Parameter describing the scattering effectiveness.

Figure 9.31: Effect of grazing angle on clutter reflectivity for different clutter types


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It can be seen from the figure that, at low grazing angles, the measurements fall below themodel because of propagation-factor effects. At high grazing angles the measuredreflectivity rises above the value predicted by the model because of quasi specular

reflections from surface facets.

For different surface types, the following are typical:

Values for between 10 and 15dB are widely applicable to land covered bycrops, bushes and trees.

Desert, grassland and marsh are more likely to have near 20dB Urban or mountainous regions will have near 5dB

These values are almost independent of wavelength and polarisation, but they only applyto modelling of mean clutter reflectivity.

9.12.2.Measured Clutter Reflectivity at 95GHz

Figure 9.32: Reflectivity of grass and crops at 95GHz

Figure 9.33: Reflectivity of deciduous trees at 95GHz


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9.12.3.Sea Clutter

Figure 9.34: Effect of grazing angle on sea clutter reflectivity

When the model is applied to sea clutter, averaging over all wind directions, it is foundthat depends on the Beaufort wind scale KB and the wavelength according to thefollowing empirical relationship,

64log106log10 = BK . (9.19)

At low grazing angles there is also a component that is a function of the polarisation

Table 9.5: The Beaufort Scale

Beaufort No Description Wind Speed (kts)

0 Calm 64


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This operational mode can be extended to encompass the measurement of the returnsfrom walls and trees if the appropriate geometry is applied, and the tree surface isassumed to be impenetrable by the radar signal.

One alternative is to gate the radar signal in range, but once again, this is not satisfactoryunless a well defined surface is being measured as shown in the range gate limited casebelow:

Figure 9.36: Definition of a pulse-width (range-gate) limited resolution cell

If the projected pulse width is sufficiently short compared to the length of the elliptical

footprint defined by the elevation beam width, then the area can be approximated by arectangle, and the formula for the area,A, is

sec

2tan

= AZ

RcA , (9.23)

where c is the speed of light (3108 m/s) and the transmitted pulsewidth (sec).

9.14.Calculating Volume BackscatterAn analogous normalisation parameter to

o exists for volume scatterers in the

atmosphere such as dust particles or raindrops. It is called .

- RCS of illuminated volume / illuminated volume (m2/m

3).

For the measurement of foliage or rain where some penetration occurs, then the volumeclutter formulation is appropriate. In this formulation an analogous normalisation

parameter to o

called exists for volume scatterers. This volume reflectivity is definedas the RCS per unit illuminated volume (m2/m3).


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As with the surface cases, the illuminated volume can be calculated from the geometry

shown below, which is just the volume of an elliptical cylinder with diameters RAZ and

REL and with length c/2.

2

2

8

cRV ELAZ= (9.24)

Figure 9.37: Definition of a volume-clutter resolution cell

The radar cross section is then the product of the volume reflectivity and the volume Vas follows:

V = (9.25)

This model assumes that there is minimal attenuation of the radar signal over the lengthof the cell. This may be a valid assumption at lower frequencies where foliage and rainpenetration is good, but it is not in the millimetre-wave band where the measured twoway attenuation in dry foliage exceeds 4dB/m and is even higher in dense green foliage.In this case a more complex formulation to take this attenuation into account is required.

( ) cV = exp

(9.26)

This can be rewritten using the more common dB notation to take advantage of the factthat attenuation is most often given in that form.

( ) cVdB = 10log10 (9.27)


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9.14.1.RainThe graphs below show the theoretical values for the reflectivity as a function of rainfall

rate at different frequencies.

Figure 9.38: Theoretical raindrop reflectivity vs rainfall rate using Marshall Palmer drop size

distribution

This data is determined using the relationship between the reflected and incident poweron small spherical targets as discussed earlier in the section on the RCS of a sphere.Though a given rainfall rate does not imply a specific drop-size distribution, the trendthat the drops get bigger as the rainfall rate increases, generally holds true.

In the Rayleigh region (D/< 1), the RCS is given by the following formula

4

62524

D

KS

SR

inc

refl == , (9.28)

2

1

+=

K , (9.29)

where - Relative dielectric constant of the material,D Diameter of the scattering object,

- Wavelength.


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When D/> 10 the equation for RCS reduces to the geometric optics form

4

2D = . (9.30)

These equations can be combined with the density of particles in the medium to

determine the total reflectivity, .

=

=N

i

i

1

. (9.31)

9.14.2.DustThe volume of dust that can be supported in the atmosphere is extremely small, and sothe reflectivity can often be neglected for EM radiation with wavelengths of 3mm ormore. However, under certain circumstances, if the dust density is very high (such as inrock crushers) or if the propagation path through dust is very long (in dust storms), then itcan be useful to determine the reflectivity and the total attenuation.

Figure 9.39: Backscatter from dust after explosion (a) at 10GHz and (b) 35GHz


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9.15.Estimating the Backscatter of Radar SignalsThe effectiveness of a ranging sensor, such as a radar or lidar, is dependent not only onthe actual signal level returned from the target of interest, but also the relative level ofthis signal in comparison to other competing returns at the same range.

The most common sources of clutter are returns from dust or water droplets within theradar beam, or from large (high reflectivity) returns that enter through the sidelobes of theantenna.

Expanding on the equations described in the previous section, it can be shown that thereflectivity for a cloud of dust particles using the Rayleigh approximation is

ZKo2

4

5

= , (9.32)

where Ko is related to the relative dielectric constant of the particle and the Z factor isdetermined from the number and size of the particles

22

02

1

+=

K , (9.33)

=i

ii DNDZ6 , (9.34)

where Ni(D)D is the number of dust particles whose diameters are between Di andDi+D, is the complex dielectric constant of the particle.

The equation forZcan be re-written in terms of the total number of airborne particles perunit volumeNTandPi which is the probability that a dust particle has a diameter between

Di andDi+D, per unit volume2,

i

i

iT PDNZ = 6 . (9.35)

The total number of particles per unit volume can also be expressed in terms of the mass

loading

33

3

4

3

4i

i

iT

i

ii rPNrNM == . (9.36)

2 Also called the number fraction distribution


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As discussed in Chapter 8, in a dust storm the visibility can be related to the mass loadingof dust per cubic meter of air by

V

CM=

(9.37)

where Mis the mass loading of dust in g/m3, Vis the visibility in metres and Cand are

constants that depend on the particle type and the meteorological conditions. Typical

values for these constants are C= 37.3 and = 1.07.

Using the mass loading formulation in the equation above and solving for NT thefollowing is obtained

==i

ii

i

ii

TrPVrPV

C

N 307.1

9

3

1025.21

.

1

..4

3 . (9.38)

Substituting

=

i

ii

i

ii

rP

DP

VZ

3

6

07.1

91025.2(9.39)

Estimates are made for the two summation terms based on typical size distributions

determined for sandstorms

=i

ii rP143 104 (m3),

=i

iiDP246 102 (m

6).

Substituting back to obtain a formula for the backscatter,

07.1

192

4

5 10125.1.

V

Ko

=

(m

2/m3). (9.40)

The following figure shows the reflectivity plotted for coal dust and for water spray withidentical particle/droplet size distributions.


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Figure 9.40: Backscatter from coal dust and water with identical particle size distributions as a

function of the visibility at 94GHz

As the frequency is increased and the backscatter mechanism moves out of the Rayleighregion into the Mie region, total backscatter increases significantly and the mediumbecomes more opaque. This is the reason that clouds look white at optical frequencieswhereas even heavy rain is more transparent even though the mass loading of rain oftenhigher than that of clouds

Under most circumstances the optical visibility through the medium is a good indicationof the performance in the near IR, so the rule-of-thumb that states if you can see thetarget, a lidar sensor can measure the range holds.

9.16.References[1] M.Skolnik (ed),Radar handbook, McGraw Hill, 1970.[2] N.Currie (ed),Radar reflectivity Measurement, Techniques and Applications, Artech, 1989.[3] D.barton, Modern Radar Systems Analysis, Artech, 1988[4] M.Skolnik,Introduction to Radar Systems, McGraw Hill, 1980[5] H.Durrant-Whyte, Sensors and Signals Notes.[6] Principle of a Pulsed Laser Sensor, http://www.riegl.co.at, 26/02/2001.[7] D.Fulghum, Stealth Retains Value, But its Monopoly Wanes, Aviation Week and Space

technology, Feb. 5, 2001.[8] Stealth Foiled by Cell Phones, http://www.smh.com.au/news/0106/12/world/world2.html, June 13,

2001.[9] P.Bhartia, I.Bahl, Millimeter Wave Engineering and Applications, John Wiley & Sons, 1984[10] Principle of a Pulsed Laser Sensor, http://www.riegl.co.at, 26/02/2001.[11] D.Barton,Radar Systems Analysis, Artech 1976.[12] C.Currie (ed), Principles and Applications of Millimeter Wave Radar, Artech, 1987.[13] H. Jensen et. al., Side-Looking Airborne Radar, Scientific American, October 1977.

09 target and clutter characteristics

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